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A002689 Denominators of coefficients for repeated integration.

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%I A002689 M4072 N1687 #26 Oct 19 2023 08:24:43
%S A002689 2,6,8,180,32,10080,3456,453600,115200,47900160,71680,217945728000,
%T A002689 36578304000,2241727488000,45984153600,2000741783040000,918421504,
%U A002689 43667471941632000,5751865147392000,240857298809487360000
%N A002689 Denominators of coefficients for repeated integration.
%D A002689 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002689 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002689 Vincenzo Librandi, <a href="/A002689/b002689.txt">Table of n, a(n) for n = 0..200</a>
%H A002689 H. E. Salzer, <a href="http://dx.doi.org/10.1080/14786444708521604">Table of coefficients for repeated integration with differences</a>, Phil. Mag., 38 (1947), 331-336.
%H A002689 H. E. Salzer, <a href="/A002206/a002206_1.pdf">Table of coefficients for repeated integration with differences</a>,  Phil. Mag., 38 (1947), 331-336. [Annotated scanned copy]
%F A002689 a(n) = A002207(n)/(n+1).
%p A002689 seq(denom(int(mul(p-i,i=0..(n-1)),p=0..1)/(n-1)!),n=1..30);
%t A002689 max = 19; a[n_] := Denominator[Sum[BernoulliB[j]/j*StirlingS1[n, j-1], {j, 1, n+1}]*(n+1)/n!]; Table[a[n], {n, 0, max}] (* or *)
%t A002689 a[n_] := Denominator[SeriesCoefficient[1/x - 1/Log[1+x], {x, 0, n}]] /(n+1); Table[a[n], {n, 0, max}] (* _Jean-François Alcover_, Apr 09 2014, after _Paul Curtz_ *)
%K A002689 nonn,frac
%O A002689 0,1
%A A002689 _N. J. A. Sloane_
%E A002689 Corrected and edited by Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 01 2010